Copyright Steven Jay Gilbert, 2000 All rights reserved.

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1 UNIVERSITY OF CALIFORNIA, SAN DIEGO A New Ultra-Cold Positron Beam and Applications To Low-Energy Positron Scattering and Electron-Positron Plasmas A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics by Steven Jay Gilbert Committee in charge: Clifford M. Surko, Chair Robert Continetti Andrew Kummel Thomas O'Neil Arthur Wolfe 2000

2 Copyright Steven Jay Gilbert, 2000 All rights reserved.

3 The dissertation of Steven Jay Gilbert is approved and it is acceptable in quality and form for publication on microfilm. Chairman University of California, San Diego 2000 iii

4 This thesis is dedicated to my life-mate, Anne. iv

5 Contents Signature Page iii Table of Contents v List of Figures vii Acknowledgments ix Vita, Publications and Fields of Study xi Abstract xiii 1 Introduction Positron Sources Moderators to Produce Low-Energy Positrons Positron Physics at Lower Energies Overview of the Thesis General Description of the Experiment Charged Particle Motion in a Magnetic Field Source and Moderator Beam Extraction and Transport Positron Accumulation Retarding Potential Analyzer (RPA) Bright, Cold Charged Particle Beams Introduction Experimental Setup Positron Beams Electron Beams Chapter Summary Positron Scattering from Atoms and Molecules Introduction Experimental Setup Data Analysis Elastic DCS Analysis Measurement of Total Inelastic Cross Sections v

6 4.3.3 Total Cross Sections Experimental Results Differential Cross Sections Total Inelastic Cross Sections Recent Results Measurements Using a Magnetic Beam Further Considerations Chapter Summary The Electron-Positron Beam-Plasma Instability Introduction Description of the Experiment Positron Plasma Parameters Cold Electron Beam Parameters Beam-Plasma Experiment Results Chapter Summary Conclusion Summary Future Work Cold Beams Positron Atomic and Molecular Scattering Electron-Positron Plasmas Concluding Remarks References 74 vi

7 List of Figures 2.1 Charged particle motion in a magnetic field Schematic diagram of the positron source and moderator Schematic diagram of the positron source vacuum chamber Schematic diagram of the three-stage positron accumulator Buffer gas pressure in the third stage during pump out Calculated pressure profile along the three-stage accumulator Schematic diagram showing the three-stage accumulator and surrounding vacuum chamber Energy distribution of a moderated positron beam Schematic diagram of the beam formation experiment Pulse train of 60 positron pulses Energy distribution of a positron pulse Potential distribution in cylindrical trap Energy distribution of a 0.1 μa quasi steady-state electron beam Current waveform of an electron beam Schematic diagram of scattering apparatus and pressure profile Scattering in a magnetic field Simulated effects of scattering on the beam energy RPA data for positron-argon elastic scattering Differential elastic cross sections for positron-krypton scattering Differential elastic cross sections for positron-argon scattering RPA data for a positron-cf 4 inelastic scattering event Positron-CF 4 inelastic cross sections Positron-CO inelastic cross sections Positron-CH 4 inelastic cross sections Positron-CO 2 inelastic cross sections Total cross sections for positron CF 4,CH 3 F, and CH Experimental limitations Effects of time resolving the DCS measurement Schematic diagram of the beam-plasma experiment vii

8 5.2 Beam and plasma radial density profiles Density distribution of the positron plasma Potential profile along the quadrupole traps axial symmetry RMS data showing the excitation of the transit-time instability Growth rates for the beam-plasma instability viii

9 Acknowledgments Iwould like to thank all of the people who helped me through the ups and downs of my graduate career. It goes without saying that the single most influential person in shaping my progress through the graduate program was my advisor, Profesor Cliff Surko. The process of choosing a graduate advisor is part research, part intuition, and part luck. I sought out someone who could guide me through all of the difficulties of a graduate research program. Cliff turned out to be an excellent choice in every respect. He has subtly taught me over the years how to get through, over, or around the many brick walls which arise during the experimental process. Along with Cliff, I am indebted to all of the people I had the pleasure of working with in his lab. Thanks to Greg, Christof, Koji, James, Gene, Rod, Chris Lund, Chris Kurz, and Judy. Special thanks to Chris Kurz, a wonderful mentor who introduced me to the art of experimental research, and helped greatly on the work presented in this thesis relating to the cold-beam formation. Researcher Rod Greaves offered his keen insight into both experimental design and the physical processes at work. Thanks to him I have gained confidence in my ability to design, build, and implement an experiment from the ground up. None of this work could have been done without Gene Jerzewski's expert technical assistance. He is a true Zen master of the lab. Despite the many attempts of the lab to break down, he was always there with a smile to tell me not to worry, that it could be fixed, and he was always right. For thelastyear James Sullivan has educated me in the ways of an atomic-physicist. He has also helped to take much of the recent data presented in Chapter 4, while I have been hunched over the computer writing this dissertation. On a personal note, I would like tothankmy family and friends for keeping me mostly sane through it all. Thanks to Mom, Eric, Dad, Pauline, Dennis, Nancy, Debbie, Mike, Stefanie, Jordan, Nan, and Ken, who complete one of the greatest families ever. Most of all I would like to thank Anne, for sticking so close to me through the thick and thin of it all. She has been a great source of inspiration and the Ph.D. degree is as much hers as it is mine. Iwould also like to thank my mother for teaching me that the day todayofwork was something to be enjoyed not wished away until the next weekend or vacation. She also never discouraged me from asking why, no matter how many frustrating times I posed the question, and this is what led me into the sciences. Iowe my sense of perspective to my brothers and sisters, although we have each pursued different things to become happy, your successes have inspired me. An integral aspect of my life has been my love of the outdoors which originated during the many walks through the woods taken with my step-farther Eric. Whether I am hiking, skiing, climbing, or biking, he will always be part of me when I am in the woods. Even though Eric started my love of the outdoors, he would never have pushed me towards rock-climbing. For that I owe my good ix

10 friend Todd, thanks for being a great teacher. Since I have been in San Diego, the Thursday-Sunday climbing group has been responsible for an uncountable number of great times outdoors. Thanks Doug, Garnet, Cindy, Frank, Mike, and all of the other wonderful people in the group. Lastly, I would like to thank the friends I have made throughout my college and graduate career for all the good times that they have given me. At the University of Rochester, I met Dylan and learned that being yourself, and remaining forever a kid was something worth striving for. At Rutgers, Amy started me on the way to making a number of life-choices, including becoming a vegetarian. Since I have been at the University ofcalifornia, San Diego, my friends Thor, Neda, and Jason, were first my study partners, and later my commiseration partners, as we all worked our way through the graduate process. Finally, thanks to Ray for sharing his enthusiasm for life, always with a stupid joke on hand. x

11 Vita May 12, 1970 Born, New Jersey, USA B.A., Physics, Rutgers University Research Assistant, University of California, San Diego M.S., Physics, University of California, San Diego Ph.D., Physics, University of California, San Diego. ARTICLES Publications 1. S. J. Gilbert, D. H. E. Dubin, R. G. Greaves, and C. M. Surko, An Electron Positron Beam-Plasma Instability," manuscript in preparation. 2. S. J. Gilbert, J. Sullivan, R. G. Greaves, and C. M. Surko, Low Energy Positron Scattering from Atoms and Molecules using Positron Accumulation Techniques," Nuclear Instruments and Methods in Physics Research B, in press. 3. S. J. Gilbert, R. G. Greaves, and C. M. Surko, Positron Scattering from Atoms and Molecules at Low Energies," Physical Review Letters 82, (1999). 4. C. Kurz, S. J. Gilbert, R. G. Greaves, and C. M. Surko, New Source of Ultra-Cold Positron and Electron Beams," Nuclear Instruments and Methods in Physics Research B 143, (1998). 5. S. J. Gilbert, C. Kurz, R. G. Greaves, and C. M. Surko, Creation of a monoenergetic pulsed positron beam," Applied Physics Letters 70, (1997). 6. K. Iwata, R. G. Greaves, C. Kurz, S. J. Gilbert and C. M. Surko, Studies of positron-matter interactions using stored positrons in an electrostatic trap," Materials Science Forum 24, (1997). 7. C. M. Surko, K. Iwata, C. Kurz, and S. J. Gilbert, Atomic and Molecular Physics using Positrons in a Penning Trap," Photonic, Electronic and Atomic Collisions, F. Aumayr and H. P. Winter, eds. (World Scientific, 1997), pp xi

12 INVITED TALKS ffl S. J. Gilbert, Low-energy Positron Scattering from Atoms and Molecules," 10th Workshop on Low-Energy Positron and Positronium Physics (a satellite conference of the International Conference on the Physics of Electronic and Atomic Collisions), Tsukuba, Japan (1999). Major Field: Physics Fields of Study Studies in Atomic and Molecular Physics Professor Clifford M. Surko Studies in Plasma Physics Professor Clifford M. Surko Studies in Positron Physics Professor Clifford M. Surko xii

13 ABSTRACT OF THE DISSERTATION A New Ultra-Cold Positron Beam and Applications To Low-Energy Positron Scattering and Electron-Positron Plasmas by Steven Jay Gilbert Doctor of Philosophy in Physics University of California, San Diego, 2000 Professor Clifford M. Surko, Chair A new technique was developed to generate intense, cold, magnetized positron and electron beams. The beam is formed by extracting particles from a thermalized, room-temperature, single-species plasma confined in a Penning trap. Cold positrons with an energy spread of 18 mev can be produced either in a pulsed or continuous mode at energies ranging from < 50 mev upward. Cold, quasisteady-state electron beams have also been generated with electron currents of 0.1 μa forseveral milliseconds using this method. These cold beams have been used to study both positron-matter interactions and electron-positron plasma interactions. Positron-atom differential cross-sections (DCS), positron-molecule total vibrational excitation cross sections, and total scattering cross sections are presented. Absolute values of the DCS for elastic scattering from argon and krypton are measured at energies ranging from 0.4 to 2.0 ev and agree well with theoretical predictions. The first low-energy positron-molecule vibrational excitation cross sections were measured (i.e., for carbon tetrafluoride at energies ranging from 0.2 to 1 ev), and recent extensions of this work to CO, CO 2,and CH 4 are described. Total cross section measurements at the lowest positron energies (i.e., down to 50 mev) are also discussed. The electron-positron plasma study consists of an electron beam transmitted through a positron plasma stored in a quadrupole Penning trap. The transit-time instability, which isexcitedby the beam, was studied from onset through the maximum in growth rate. The experimental results are compared with the results of a new cold-fluid model and are in good agreement over a broad range of energies and beam currents. xiii

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15 Chapter 1 Introduction Positrons were first predicted by Dirac [20] in 1930 and discovered soon after by Anderson in 1932 [3, 4]. Anderson made his discovery by studying tracks of cosmic rays in a cloud chamber. He noticed a particle with a positivecharge that appeared to be lighter than both the proton and the alpha particle (the only known positive particles at the time). The new particle appeared to have the same mass as an electron. Anderson called this new particle a positive electron or positron. Two years later Joliot generated the first man-made radioelement, and coincidentally the first man-made positron source, by bombarding a thin sheet of aluminum with alpha particles [57]. The isotope 30 P that he created decays into a stable isotope of silicon by emitting a fi + (i.e., a positron) and a neutrino. Thus, Joliot developed the first radioactive source of positrons. Advances in positron sources progressed quickly after Joliot's discovery, generating stronger sources with longer life times. Since the discovery of the positron [3], it has been clear that the study of positron interactions with matter is an important and insightful area of physics research. In order to study positron interactions with matter experimentally, two criteria must be met. The first is that the signal-to-noise ratio of the experiment must be sufficiently large. The second is that the energy and or spatial resolution of the positrons must be small enough for these results to be meaningful. The signal-to-noise ratio in a positron-matter experiment istypically related to the abundance of low-energy positrons and the efficiency of their detection. Positrons can either be detected using a scintillator, which detects the fl-ray emitted when the positron annihilates with an electron, or by measuring the positron charge using a charge multiplier. In either case, low-noise positron detectors with near unity efficiency are more-or-less conveniently available. 1

16 2 Chapter Positron Sources Positron sources of sufficient yield to perform experiments have been available almost since the discovery of the positron. Currently, there are two methods for producing a high intensity positron source. Positrons can either be created using a linear accelerator (LINAC) [1, 48, 101] or a radioactive isotope. A LINAC produces positrons by bombarding a high-z material such as tantalum with high-energy electrons (ο 100 MeV). The rapid deceleration of the electron generates Bremsstrahlung fl rays, which in turn create electron-positron pairs. The positrons are then extracted and formed into a positron beam. The main advantage of a LINAC-based positron source is that the intensity can be very high (i.e., > positrons/s). Disadvantages of using a LINAC-based positron source include an electrically noisy environment generated during the high-energy electron pulse, limited availability of LINAC facilities, and relatively high capital and operating costs. Radioactive positron sources have improved considerably since Joliot's discovery of a phosphor source with a three minute half-life. The most common sources in use today are 22 Na, 68 Ge, and 58 Co. The main advantages of using a radioactive source are that they are relatively inexpensive (e.g., compared to a LINAC source), small, and can be self contained. A self contained source is critical for the accumulation and trapping of positrons used in the experiments described in this thesis. The positron accumulation efficiency is very sensitive to impurities, such as hydrocarbons, and so having to connect the vacuum chamber to another vacuum system, such as a LINAC, would make maintaining a hydrocarbon free system more difficult. A 22 Na source is used in the experiments described in this thesis. It has a 2.6 year half-life and is attainable with activities up to 150 mci. The only disadvantage to using a radioactive source over a LINAC based positron source is a lower positron intensity (ο 10 9 positrons/s for 150 mci 22 Na source vs for a LINAC). For our experiments, the advantages clearly outweigh the disadvantages making a radioactive source an attractive choice. Positrons emitted from either radioactive sources or particle accelerators have a broad energy spread ranging up to several hundred kev and therefore need to be slowed down before they can be effectively used in a positron-matter experiment. Unfortunately, advances in producing mono-energetic positrons were not as forthcoming as advances in positron sources. In fact, as late as 1969 in a review on the theory of `Positron Collisions', Bransden lamented that: the points of contact between the experiments and theory are not as many as could be wished and are somewhat indirect. The reason for this is that, in contrast to the electron in positron scattering, there are at present no controlled mono-energetic beams of lowenergy positrons [8].

17 Introduction Moderators to Produce Low-Energy Positrons In 1972, Costello et al. made a critical breakthrough, finding evidence that fast positrons impinging on a gold surface are slowed to a few electron volts and then ejected from the surface [17]. This resulted in a practical technique to produce a low-energy positron beam. Not long after this, improvements on the gold moderator were made by Coleman et al. [15] and then further improved by Canter et al. [11]. These discoveries led to the first low-energy positron beams used in positron-matter experiments, which were measurements of the total cross sections for low-energy positron-helium collisions [11]. Canter's moderator consisted of a system of gold vanes. Each vane had a fine MgO powder deposited onto it, increasing the moderating efficiency by a factor of 10 from that of the gold vanes alone. A positron beam of variable beam energy was produced by extracting the moderated positrons through an electrostatic field. The final moderator had an energy spread of 1.5 ev FWHM and a yield of ffl ο 10 5,whereffl is the ratio of low energy positrons extracted from the moderator to the high energy positrons impinging on the moderator. Work on producing more efficient positron moderators has progressed continually since Canter's work [11]. Single crystal metal moderators, such as tungsten [33], nickel [110] and copper [77] have efficiencies as large as ffl ο Tungsten is especially appealing because of its narrow energy distribution, 0.3 ev FWHM, making possible some of the highest resolution positron-matter experiments to date [60, 100]. The introduction of solid rare-gas moderators in the 1980s improved positron moderator efficiencies by another two orders of magnitude [80]. The most efficient rare-gas moderator to date is made by freezing neon gas onto a metal surface at ο 8 K. For the experiments described in this dissertation, a solid neon moderator was used. It has an efficiency ffl ο 10 2,and an energy spread of 1 ev FWHM. Until the work presented in this thesis, almost all efforts to reduce the energy spread in the available positron beam sources and to increasing positron brightness have been focused on improved moderator schemes. One successful method is through the use of remoderators. It has been shown that positron moderator efficiency increases as the energy of the incident positron decreases, and can be as large as ffl ο 0:3 fora3kev incident positron [9]. There is also evidence that the energy distribution of the emitted positrons is nearer to that of a thermalized distribution at the moderator temperature. For example, the moderated beam energy distribution of a 3 kev incident positron beam on a Ni(100) moderator at 300 K and 23 K is 80 mev and 24 mev FWHM, respectively [25]. Unfortunately the moderation efficiencies are greatly reduced as the moderator temperature is decreased [9], and so a cold beam can only be generated using this technique at the expense of a low overall moderator efficiency. Another use of remoderators is to increase the positron beam brightness (i.e., flux per unit area per unit energy). This can be accomplished by accelerating

18 4 Chapter 1 and then electrostatically focusing a moderated beam onto a second moderator. The re-emitted positrons will have a spatial resolution comparable to that of the focused beam and an energy resolution ο 0:1 ev. By successive acceleration, focusing, and remoderation steps, smaller beam sizes can be achieved without the expense of increased energy spread [59]. Because of the high remoderation efficiency, the brightness of such a beam can be increased although, as mentioned above, the positron flux decreases with each remoderation step. Since Canter's positron-helium total cross section measurements [11], a large body of work has been performed to study positron-matter interactions at lowenergies. Examples in atomic physics include total cross section and positron annihilation rate measurements, inelastic cross sections for positronium formation, excitation and ionization of atoms, and differential elastic scattering cross sections. Excellent reviews on positron-atom and positron molecule cross sections measurements can be found in Refs. [12, 53, 60]. An account of the earlier work on measurements of total cross sections can be found in Refs. [40,73]. There have also been great advances in the study of surfaces using slow positron beams, including defect-depth profiling, low energy positron diffraction and reflection, and high-energy positron diffraction [78, 94]. 1.3 Positron Physics at Lower Energies Despite these developments, there is still a largely unexplored region of energy (i.e. < 1 ev) which cannot be studied easily using the existing moderated beams. This is a very interesting energy regime. For example, in atomic physics many important processes occur at these low energies, such as vibrational [19, 28, 62] and rotational [30] excitation of molecules, which have not yet been experimentally studied by positron impact. The low-energy interaction of positrons and ordinary matter is important in fields such as astrophysics, atomic physics, and chemical physics. Exploring this energy regime should provide important new information, such as understanding the role of virtual positronium states in positron interactions with matter [53], the mechanisms by which positrons bind to atoms and molecules [39], and the process of large molecule fragmentation by positrons [47, 89]. 1.4 Overview of the Thesis This thesis describes a new technique to produce a state-of-the-art mono-energetic positron beam [32, 65]. To form a cold beam, positrons are first accumulated in a Penning trap where they thermalize to room temperature through collisions with a background gas. These cold positrons are then extracted from the trap by decreasing the depth of the potential well confining them, thus forcing the cold positrons out of the potential well and into a beam. The beam has an energy

19 Introduction 5 distribution of 18 mev FWHM, and it can be tuned over a wide range of energies from < 50 mev upward. Both pulsed and steady-state beams can be produced depending on the requirements of the experiment at hand. Positron throughput is > positrons/s, and in pulsed operation, the beam brightness is greater than that achieved using two remoderation stages [94]. This thesis also describes the first uses of this new beam in two areas of positron-matter interactions. The first is a study of positron-atomic and positronmolecular physics at energies below 1 ev. We have measured the differential cross sections for positron collisions with argon and krypton at energies below that of any previous measurement. We have also made the first measurements of the cross sections for vibrational excitation of molecules by positrons, studying the excitation of CF 4 at positron energies as low as0.2 ev. Most recently we have extended our study of positron-molecular vibrational cross sections to include CO, CO 2, and CH 4. We have also recently studied the total cross section for positron-molecule scattering at energies from 50 mev to several electron volts, which represents a higher energy resolution measurement than any previous work. Both the technique developed to produce the cold positron beam and the new method to measure scattering cross sections are in the early stages of development. We expect improvements in both will continue to extend our ability to explore atomic and molecular physical processes at energies below 1eV. The second area of positron-matter interactions we have examined using the cold beam is the study of electron-positron plasmas. Because of difficulties in simultaneously confining both positrons and electrons, the simplest experimental arrangement in which electron-positron plasma interactions can be studied is an electron beam passing through a positron plasma. The unique ability to accumulate and store large numbers of positrons that the group has developed greatly facilitates this kind of experiment. The work by Greaves et al. [34] was the first experimental study of this system; it was done by transmitting an electron beam through positron plasmas stored in Penning traps with both cylindrical and quadrupole potential wells. In these experiments, a conventional hot-cathode electron gun was used as the electron beam source. Unfortunately, the large energy spread of the hot-cathode electron gun restricted beam-plasma studies to energies above ο 1eV. Although conventional means to create mono-energetic electron beams are available, they do not work in the high magnetic field (ο 1 kg) necessary to confine the positron plasma. Wehave been able to apply the same technique used to produce cold positron beams to generate cold electron beams. Because this technique was designed to operate in the high field needed for the beam-plasma experiments, it was an ideal way to carry out the beam-plasma experiments at the lower beam energies where the maximum growth rate and instability onset were predicted to occur. This thesis discusses research using the cold electron beam to investigate further the instability generated by passing a cold electron beam through a positron plasma confined in a quadrupole well. We

20 6 Chapter 1 were able to study the instability down to beam energies as low as ο 0:2 ev, which corresponds to the onset of the instability. The organization of the thesis is as follows. Chapter 2 discusses specific details of the experimental apparatus which pertain to all of the experiments described in this thesis. The technique used to generate cold positron and electron beams is presented in Chapter 3 along with specific characteristics of the types of beams. Chapters 4 and 5 describe new experiments using the cold beams to study positron-matter interactions. In Chapter 4 positron-atom and positronmolecule studies are described in the largely unexplored range of energies below 1 ev. Positron-electron plasma physics studies are described in Chapter 5, in the form of an electron-beam positron-plasma transit-time instability. Finally, a summary of the work and concluding remarks are presented in Chapter 6.

21 Chapter 2 General Description of the Experiment This chapter describes the apparatus and techniques used which are common to all aspects of the experiments discussed in this thesis. Positrons emitted from a radioactive 22 Na source are moderated to low energies and magnetically guided into a three stage Penning trap used to accumulate the positrons. The entire system is enclosed in a ultra-high vacuum (UHV) chamber, which has achieved pressures as low as torr. A confining magnetic field is generated using a number of solenoids which surround the vacuum vessel. The field varies from ο 200 G in the source chamber and beam tube up to 1500 G in the accumulator, where a high field is necessary for good positron confinement. Once a plasma is accumulated it is either used as a reservoir to form a cold beam as described in Chapter 3, or as a cold plasma in a beam-plasma experiment (see Chapter 5). The apparatus described in this chapter has been completely redesigned from the knowledge gained by operating an earlier version of a positron accumulator. A detailed description of the earlier accumulator can be found in Ref. [84]. Some of the work described in this thesis was done using the earlier apparatus. In these cases, a note will be made in the text that the earlier accumulator was used, and any additional information pertaining to the particular experiment is given. However, in most cases, the operation of these two machines is similar enough to not warrant this. 2.1 Charged Particle Motion in a Magnetic Field Because all of the experiments described in this thesis are conducted in a magnetic field, it is helpful to briefly review charged particle motion in such a field. The most basic motion is that of a charged particle moving through a constant magnetic field. Figure 2.1 shows a schematic diagram of this motion. The particle follows a helical orbit which can be conveniently split into two distinct 7

22 8 Chapter 2 Figure 2.1: Charged particle motion in a magnetic field. The helical path can be separated into a circular motion in the plane perpendicular to the field and a linear motion along the field. The total kinetic energy, E, of the particle is the sum of the kinetic energy associated with motion along the field, E k, and the kinetic energy due to the circular motion, E?, where E = E? + E k. motions, a linear motion along the magnetic field and a circular motion in the direction perpendicular to the field. The radius of this orbit, known as the cyclotron radius r c, is proportional to the particle velocity and inversely proportional to the magnetic field strength. Specifically, r c = mv? =eb, where m, is the charged particle mass, v? is the particle velocity perpendicular to the magnetic field, e is the charge, and B is the magnetic field strength. For example, p a typical positron in our cold positron beam (see Section 3.3) will have v? ο 2kT=m, where kt is the thermal energy of the room temperature positrons (ß 0:025 ev). The cyclotron radius of such a positron when placed in a 0.1 tesla field will therefore be, r c ο 5 μm, which has been greatly exaggerated in Fig. 2.1 to show the helical motion. It is convenient to split the total particle kinetic energy into the components due to these two motions. We express the total energy of the particle as E = E? + E k, where E k is the kinetic energy along the magnetic field and E? is the kinetic energy in the circular motion perpendicular to the magnetic field. Chapter 4 describes how this convention simplifies the analysis of the scattering events in the strong magnetic field. When the magnetic field strength varies as a function of position, the trajectory of the charged particles can be described with the help of a useful adiabatic invariant. The ratio E? =B is adiabatically invariant as long as the distance over which the magnetic field strength changes appreciably is small compared to the cyclotron radius. For example, as a charged particle moves into a region of decreasing magnetic field E? must decrease. Conservation of energy implies that E k must therefore increase. As the particle continues to move intoaweaker field, E k increases until nearly all of the particles energy is in E k. At this point the charged particle is moving almost directly along the magnetic field with a very small cyclotron radius. Section describes how we take advantage of the adiabatic invariant to determine the total vibrational cross section of a positron-molecule scattering event.

23 General Description of the Experiment 9 Lastly, when the lines of magnetic induction curve, and the radius of curvature R is large compared to the cyclotron radius, the zero-order approximation to the motion of the particle in the field is to follow the lines of force. For the experiments described here this approximation always holds, and therefore the guiding center of the particles, to zero-order, always follows the magnetic field. To first-order there is a drift velocity in the guiding center motion, associated with the curvature R. This motion, which is in a direction perpendicular to the magnetic field, is too small to effect the particle trajectory in a single pass, for example, when transferring the positrons from the source to the accumulator (see Section 2.3). When the particles make many passes through a curved region of field the accumulative drift can be quite large. For this reason, the magnetic field is highly uniform throughout the positron accumulator, therefore minimizing any drifts which would reduce the confinement time of the trapped positrons. 2.2 Source and Moderator There are several possible approaches to generating the slow positron beams necessary for trapping and accumulation [88, 94]. In all of these approaches the positrons originate from either a radioactive source or from a particle accelerator. In the case of radioactive sources, one of the most intense positron producers is 64 Cu. Although the fast-positron count rate for 64 Cu is quite large ( e + =s), the production requires a reactor with a high thermal neutron flux and must be generated daily because it has a half-life of only 12.8 h [69]. For these reasons, we have chosen to use the more practical radioactive positron source 22 Na. 22 Na has many properties which makeitagoodchoice, most importantly it has a high branching ratio of 90%, a long life time, and is commercially available. The 22 Na positron source that is used in the experiment was obtained from DuPont Merck Pharmaceuticals in September 1997 with a source strength of 150 mci and a quoted efficiency of 70% of the 2ß value. The 22 Na source has a half life of 2.6 y and emits a broad energy range of positrons with a fairly continuous spectrum up to 540 kev. The source is sealed in a titanium capsule used to isolate it from the vacuum system. The current source efficiency is reported to be a factor of two higher than past efficiencies. This improvement is obtained by increasing the purity of the source material, and therefore reducing positron annihilation. In order to slow the kev positrons to ev energies a moderator is needed [13, 41, 79, 80, 94]. Positron moderators take advantage of positron interactions with solids as follows. A high energy positron hits the solid and initially looses energy by ionization or creation of electron-hole pairs. At lower energies, the positron loses energy by positron-phonon interactions and eventually thermalizes

24 10 Chapter 2 Figure 2.2: Schematic diagram of the positron source and moderator showing the positron source relative to the moderator cone. The cone is kept at ο 8Kbyatwo-stage refrigerator, which is in thermal contact through an elkonite rod with the cone. A heat shield surrounds the source and cone to reduce the radiative heat loss. with the solid. Because the time it takes for the positron to thermalize (ο s) [64] is short compared to their annihilation lifetime, a fraction of the thermalized positrons can diffuse (via positron-phonon collisions) to the surface. By using a solid with a positive work function, a portion of these positrons are then ejected from the solid with an energy comparable to the positron work function of the solid. There are a number of different types of moderators in use. Single-crystal metal moderators, such as tungsten [33], nickel [110] and copper [77] were originally used, and have efficiencies as large as ffl ο More recently rare-gas solid moderators such as neon have been shown to have much higher efficiencies (ffl ο 2: ) [35], and are therefore used in these experiments. The minor draw-back of a larger energy spread (ο 1 ev FWHM in the neon moderator vs. ο 0:3 ev FWHM for the tungsten) is not an important factor because the positron accumulator (see Section 2.4) is almost as efficient at trapping a positron beam generated from the neon moderator as it is from the tungsten moderator [52]. Figure 2.2 is a schematic diagram of the source and moderator arrangement. The 22 Na source is located in a titanium capsule which has a 13 μm titanium window welded onto its front. The titanium capsule is attached to an elkonite rod (tungsten-copper alloy used for its high thermal conductivity and good fl-ray shielding abilities), which is, in turn, attached to a two-stage refrigerator. An

25 General Description of the Experiment 11 Figure 2.3: Schematic diagram of the positron source and moderator vacuum chamber showing the source and moderator mounted to the two-stage refrigerator. The source assembly is offset from the beam tube to block the line of sight from the source to the accumulator. A magnetic field generated by a set of pancake coils and a vertical coil guides the moderated positrons into the beam tube. Radiation from the source is blocked by lead bricks, which surround the vacuum chamber. OFHC aluminum cone is screwed on over the titanium capsule and serves as a cold surface to form a frozen neon moderator. The cone is in thermal contact with the second stage of the refrigerator and is typically cooled to ο 8 K, which is measured using a calibrated silicon diode. Thermal regulation is obtained by a heating coil located on the refrigerator and a control feedback system. To reduce the heat load on the second stage, a heat shield (35 K) surrounds the entire source/moderator assembly and is in thermal contact with the first stage of the refrigerator, which has a greater heat capacity. Aschematic diagram of the UHV vacuum chamber that houses the source and moderator is shown in Fig The vacuum system is pumped by aion pump and has a typical base pressure of ο torr. The positron moderator is generated by introducing neon gas directly in front of the 8 K moderator cone (see Fig. 2.2). We have no direct measurement of the neon gas pressure near the moderator cone, and instead regulate the pressure using a stable ion gauge located in the UHV chamber. The pressure outside is maintained at ο torr, and one can assume that the pressure near the cone is much higher. The moderated positron count rate is monitored as a function of time during the grow cycle by a small fl-ray detector located near the beam tube, and the growth cycle is stopped when the positron count rate saturates, which typically takes ο 1 h. After the moderator has finished growing, its efficiency continues to rise for ο 1 h, perhaps by a rearrangement of the neon crystal

26 12 Chapter 2 structure. A moderator grown in this fashion typically yields a positron flux of ο e + /s and can last for many months. The moderator used in our earlier apparatus had a life time of ο 12 h, making the calibration of long term experiments difficult. The current improvement, which we attribute to a cleaner UHV system, eliminates this difficulty. A detailed description of the solid neon moderator apparatus and operation can be found in Ref. [35] 2.3 Beam Extraction and Transport The neon moderator is biased to ο 30 V for beam extraction and efficient positron accumulation (see Section 2.4). The moderated positrons are guided from the moderator to the accumulator by a magnetic field (ο 200 G) generated from the series of pancake coils shown in Fig Pancake coils are used so that lead shielding can be located as close to the 22 Na source as possible. To prevent the 1.27 MeV fl-rays and high-energy positrons emitted from the source from interfering with the fl-ray detectors located beyond the accumulator, the source and moderator are offset from the axis of the positron accumulator by 2 cm.a vertical coil is wound around the source chamber to transport the lowenergy positrons from the offset position onto the axis of the accumulator, while the high energy positrons and fl-rays hit the wall of the source chamber. The positrons then enter the beam tube, which is a small diameter (ο 2 cm) vacuum tube surrounded by a magnetic coil. They are then guided into the positron accumulator. 2.4 Positron Accumulation The low-energy positron beam enters the positron accumulator at a rate of ο e + /s. A specially designed Penning-Malmberg trap [38,84,104] is then used to efficiently trap the positrons. Figure 2.4 shows a schematic diagram of the modified trap used in the experiment. The trap uses a set of cylindrically symmetric electrodes to produce an electrostatic potential well that confines the positrons axially. Radial confinement is achieved with a magnetic field generated along the axis of the electrode structure. This design, which offers excellentlongterm confinement of positrons [71,86], enabled the creation of the first laboratory positron plasma in 1989 [104]. Trapping the slow positron beam as it enters the accumulator is a nontrivial task. For the case of an abundant charged particle, such as electrons, an acceptable trapping scheme is simply to raise a potential barrier when the trap is flooded with particles, thereby trapping all of the particles within the electrodes. Because electron beams with densities n b > 10 9 cm 3 are easily attained, electron plasmas with the same density can be trapped using the above technique. For the case of positrons from our 22 Na source and moderator the beam density is

27 General Description of the Experiment 13 Figure 2.4: Schematic diagram of the three-stage positron accumulator, showing the electrode structure (above), which is used to create regions with different pressures of nitrogen buffer gas by differential pumping. (below) The electrostatic potential profile used to trap the positrons. only n b > 10 1 cm 3, therefore an efficient means of accumulating positrons over a relatively long period of time must be used. To achieve this, a buffer-gas trapping scheme is used in the following manner. The moderated positrons enter the positron accumulator with a beam energy of ο 32 ev and an energy spread of ο 1 ev FWHM. A nitrogen buffer gas is introduced into the middle of the first stage of the accumulator and is pumped out at both ends. Differential pumping is used to generate three pressure regimes from 10 3 down to 10 6 torr, corresponding to the three stages. As the moderated positrons enter the first stage of the accumulator they inelastically collide with the N 2 buffer gas ( A" in Fig. 2.4) losing energy, and becoming trapped in the potential well. By making another two inelastic collisions with the buffer gas ( B" and C") the positrons move from the relatively high pressure region of stage I into the low pressure region of stage III, where they cool to room temperature (0.025 ev) in approximately 1sby further collisions with the N 2 buffer gas [38]. The most effective inelastic process for trapping the positrons is electronic excitation of N 2 by positron collision at approximately 8.6 ev. In order to max-

28 14 Chapter 2 imize the trapping efficiency via the electronic excitation, the potential well depth in each of the stages must be adjusted so that the cross section of the electronic excitation is maximized through that stage. Unfortunately, another dominant cross section which turns on at energies near the electronic excitation is positronium formation at 8.8 ev. Because positronium formation is a positron loss mechanism it is critical to operate the accumulator at energies below where this is a dominant loss mechanism. In practice, the maximum trapping efficiency is found by mapping out the trapping rate as a function of well depth and searching for a maximum. Typically the maximum efficiency occurs when the accumulator is operated with a step height between stages of V ο 9V. Another critical factor which effects the trapping efficiency of the accumulator is the buffer gas pressure profile through the three stages. In order to trap the moderated positrons the pressure in the first stage is adjusted so that the probability of an inelastic collision occurring on the first pass through the accumulator is large (labeled A" in Fig. 2.4). Once the positron has been trapped it can make multiple passes through all three stages until the inelastic collision labeled B" occurs and the positron falls into the next potential well. The pressure in stage II has to be large enough for the second transition to occur before the positron annihilates on the N 2 buffer gas in stage I. Similarly, once the positron is trapped in stages II and III, the transition into the stage III ( C") must occur before the positron annihilates in stage II. The pressure of the nitrogen buffer gas in all three stages can be adjusted as follows. The stage I pressure is controlled by adjusting the rate of nitrogen introduced into the center of the stage I electrode structure. The right end of the stage I electrode has a 5 cm long slotted section which allows some of the buffer gas to exit the stage I electrode before entering stage II. A baffle, which is externally adjustable, can slide over this slotted region restricting this flow ofgas through the slots (see Fig. 2.4). By moving this baffle from a completely closed to open position the pressure ratio between the stage I and stage II electrodes can be adjusted from 2 to 20, respectively. The stage III pressure can be altered by adjusting the flow of a second nitrogen gas line which is located near the third stage. In practice, the trapping efficiency of the accumulator is maximized by adjusting the large parameter space, which includes the accumulator electrode potentials and the pressure profile through each of the three stages, and searching for maxima. The electrode optimization is achieved using a computer assisted optimization routine [38]. The pressure optimization, which is not yet under computer control, was maximized by manually sweeping the parameter space. There are two regimes in which theaccumulator is operated. Typically the accumulator is run at its highest trapping efficiency. Figure 2.4 shows the pressures used in the three stages to achieve the maximum trapping efficiency, which for our new accumulator is ο 20%. Operating the accumulator for maximum efficiency requires a fairly high pressure in the third stage and therefore the positron life time is only ο 40 s. If a longer positron lifetime is needed the nitro-

29 General Description of the Experiment Pressure (Torr) Valve shut Valve open Time (sec) Figure 2.5: Buffer gas pressure in the third stage as the gas is cycled from its base pressure to its operating pressure and back to its base pressure. The pressure in the third stage can be decreased by three orders of magnitude in 10 s. gen buffer gas can be quickly pumped. Figure 2.5 shows the pressure in the third stage of the accumulator as the buffer gas is cycled from its operating pressure of ο torr to its base pressure of < torr in a few seconds. With the buffer gas pumped out the positron lifetime increases to 20 min, limited by impurities in the vacuum chamber. In the earlier accumulator a dewar filled with liquid nitrogen, which pumped out these impurities, surrounded a quadrupole Penning trap, and in this trap positron lifetimes of over 2 hours were possible. Currently we are constructing a high-field (5 tesla) positron storage stage, which will incorporate a 4 K cold trap around the electrode structure, with expected positron lifetimes of many hours to days (see Section 6.2.1). When a large number of accumulated positrons are needed it is more efficient to operate the accumulator with a lower pressure in the third stage. Figure 2.6 shows the results of a computer particle code used to simulate the pressure profile throughout the accumulator [5] when it is optimized for a maximum number of trapped positrons. Operating under these conditions allows the trap to accumulate positrons for over 6 min, trapping approximately positrons

30 16 Chapter III II I 10-3 pressure (Torr) z(m) Figure 2.6: Calculated pressure profile as a function of distance along the three-stage positron accumulator. The pressure profile shown here is used to maximize the total number of positrons accumulated. [37]. Aschematic diagram of the accumulator and its surrounding vacuum vessel is shown in Fig The accumulator is contained in a UHV vacuum chamber, bakeable to 130 ffi C, with a base pressure which has reached as low as torr. Two cryo-pumps located at both ends of the accumulator are used to generate the differential pumping of the buffer gas and to quickly pump out the gas when needed. The simplified design of the new electrode structure allows a single magnet to surround the entire vessel (the earlier design had two magnets), which improves the uniformity ofthe magnetic field throughout the accumulator, and simplifies the magnet alignment procedure. The accumulator is typically operated with a magnetic field of 1500 G. 2.5 Retarding Potential Analyzer (RPA) The positron and electron beam energy distributions are measured using a retarding potential analyzer (RPA). An RPA consists of an electrode at a potential of V 0 that rejects all particles with a parallel energy less than ev 0. The particles